Consider the periodic signal x(t) = cos(2 0 t) + 2 cos( 0 t), < t <

Consider the periodic signal x(t) = cos(2Ω₀t) + 2 cos(Ω₀t),−∞ < t < ∞, and Ω₀ = π. The frequencies of the two sinusoids are said to be harmonically related.

(a) Determine the period T₀ of x(t). Compute the power P_x of x(t) and verify that the power P_x is the sum of the power P₁ of x₁(t) = cos(2π t) and the power P₂ of x₂ (t) = 2cos(πt).

(b) Suppose that y(t) = cos(t) + cos(πt), where the frequencies are not harmonically related. Find out whether y(t) is periodic or not. Indicate how you would find the power Py of y(t). Would P_y = P₁ + P₂ where P₁ is the power of cos(t) and P₂ that of cos(πt)? Explain what is the difference with respect to the case of harmonic frequencies.